{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n"
     ]
    }
   ],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "import scipy.stats as stats\n",
    "import math\n",
    "from sklearn.mixture import GaussianMixture"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "mu_1 = -1\n",
    "mu_2 = 1\n",
    "variance = .3\n",
    "sigma = math.sqrt(variance)\n",
    "x = np.linspace(mu_1 - 3*sigma, mu_2 + 3*sigma, 100)\n",
    "# x = (x -np.mean(x)) / np.std(x)\n",
    "\n",
    "points = stats.norm.pdf(x, mu_1, sigma)+stats.norm.pdf(x, mu_2, sigma)\n",
    "plt.plot(x, points)\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GaussianMixture(covariance_type='full', init_params='kmeans', max_iter=100,\n",
       "        means_init=None, n_components=1, n_init=1, precisions_init=None,\n",
       "        random_state=None, reg_covar=1e-06, tol=0.001, verbose=0,\n",
       "        verbose_interval=10, warm_start=False, weights_init=None)"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gm = GaussianMixture(1)\n",
    "gm.fit(x.reshape(-1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.22044605e-17]])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gm.means_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[2.37582548]]])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gm.covariances_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.2434497875801754e-16, 1.5413709733880205)"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "mean,std=norm.fit(x)\n",
    "mean, std"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for mu, std in zip(gm.means_, np.sqrt(gm.covariances_.flatten())):\n",
    "    p = stats.norm.pdf(x, mu, std)\n",
    "    plt.plot(x, p)\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x21644f0da20>]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "points = stats.norm.pdf(x, mean, std)\n",
    "plt.plot(x, points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.DataFrame({'real': [5, 3, 4, 1], 'fake': [6, 2, 4, 1.5]})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x17f95ed62e8>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "line = [0, 7]\n",
    "sns.lineplot(x=line, y=line)\n",
    "sns.scatterplot(x=data['real'], y=data['fake'])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "data2 = pd.DataFrame({'real': [2, 4, 4, 5], 'fake': [1, 3, 4, 4]})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x17f95faa898>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "line = [0, 7]\n",
    "sns.lineplot(x=line, y=line)\n",
    "sns.scatterplot(x=data2['real'], y=data2['fake'])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.DataFrame({'real':[0.7685, 0.9859, 0.7128, 0.9237], 'fake': [0.7353, 0.9748, 0.7025, 0.9406]})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = np.abs((data.real - data.fake) / data.real)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Absolute Percentage Error')"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.barplot(x=y.index, y=y)\n",
    "plt.title('Absolute Percentage Error')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "base"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
